My jumbled thoughts -
Godzilla vs Kong definitely goes full 'monster movie.' It has a big, fun, adventurous heart, basically the super earnest Journey to the Center of the Earth/At the Earth's Core version of one of these movies. There are tons of little (and big) nods to the 1962 film throughout and for the most part I found it enjoyable and inoffensive. Kids will love it.
It does play a bit more like a straight Kong: Skull Island sequel though, just so happening to have Godzilla in it. Team Kong (Alexander Skarsgård, Rebecca Hall, Kaylee Hottle) are definitely the more fleshed out and engaging side to the story. Team Godzilla (Millie Bobby Brown, Brian Tyree Henry, Julian Dennison) and the villains (Shun Oguri, Eiza González, Demián Bichir) are broad and cartoonish. Kyle Chandler is just there, trying to figure out which movie he's in.
It has less going on than KOTM, mostly to its benefit, sometimes to its detriment – like I said; there are really broad and cartoonish moments for sure with 'convenient' problem solving for the characters. It's like King Kong vs Godzilla meets Godzilla vs Mechagodzilla meets Jules Verne meets Edgar Rice Burroughs, with lots of super-satured, Pacific Rim-esque colors.
More thoughts –
Spoiler
The storm that wiped out Skull Island could've been elaborated on more, and I guess all the Titans from KOTM are dead for whatever reason. None of the new or briefly returning monsters receive any generous screen time.
It's nice seeing a more destructive Godzilla in one of these movies for once, the monster scenes in general in either broad daylight or brightly lit, colorful cityscapes (ala Pac Rim) were more than welcome.
I don't know how to feel about the conspiracy theorist guy. I mean, first of all, it's not much of a conspiracy when giant monsters are walking around. Also, in today's climate, depicting a conspiracy theorist in a positive light might not be the best idea.
Like Kyle Chandler, Mechagodzilla is just kinda there, no real rhyme or reason for it, and quite a leap from even the Argo superjet from KOTM. He's not justified well at all in the story; he's just there cause the evil bad guy said he could build him.
Unless I missed it there's absolutely no mention of Ren Serizawa being the son of Ishirō Serizawa. He's just there too, piloting Mechagodzilla via Ghidorah's remains in a highly convoluted manner.
Godzilla drilling to the center of the earth joins stopping an artificial black hole and Monster X's meteor for most outlandish atomic breath feats. (They made a big deal entering Hollow Earth, not so much exiting.)
As a movie of this type there are several (for me, forgivable) lapses in logic, but somehow short-circuiting Mechagodzilla by splashing liquor on a computer is a bridge too far. I don't understand how that was even seriously suggested let alone kept in a final shooting script.
Thomas Holkenborg's score was serviceable but KOTM by Bear McCreary was considerably better.
Oh, and for the obligatory Marvel/DC comparison, I'd say it's nowhere as good as Captain America: Civil War, but certainly better than Batman v Superman. This movie has heart where BVS has none.